Simplify; express your answer in exponential form. Assume $r\neq 0, a\neq 0$. $\dfrac{{(r^{2})^{-1}}}{{(r^{-1}a)^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${r^{2}}$ to the exponent ${-1}$ . Now ${2 \times -1 = -2}$ , so ${(r^{2})^{-1} = r^{-2}}$ In the denominator, we can use the distributive property of exponents. ${(r^{-1}a)^{2} = (r^{-1})^{2}(a)^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(r^{2})^{-1}}}{{(r^{-1}a)^{2}}} = \dfrac{{r^{-2}}}{{r^{-2}a^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{-2}}}{{r^{-2}a^{2}}} = \dfrac{{r^{-2}}}{{r^{-2}}} \cdot \dfrac{{1}}{{a^{2}}} = r^{{-2} - {(-2)}} \cdot a^{- {2}} = a^{-2}$.